Question

What is the vertex of `y = 3/2x^2+20x+21`?

Answer 1

`"vertex "=(-20/3,-137/3)`

Explanation:

`"given a parabola in "color(blue)"standard form"`

`•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0`

`"then the x-coordinate of the vertex is "`

`•color(white)(x)x_(color(red)"vertex")=-b/(2a)`

`y=3/2x^2+20x+21" is in standard form"`

`"with "a=3/2,b=20" and "c=21`

`x_("vertex")=-20/3`

`"substitute this value into the equation for y-coordinate"`

`y_("vertex")=3/2(-20/3)^2+20(-20/3)+21`

`color(white)(xxxx)=200/3-400/3+63/3=-137/3`

`color(magenta)"vertex "=(-20/3,-137/3)`